Compare betting odds with your estimated probability to calculate the expected value of a bet.
Expected value depends entirely on the accuracy of your probability estimate. A positive EV calculation does not guarantee that an individual bet will win.
Expected value, usually shortened to EV, measures the theoretical average result of a bet based on the price being offered and your estimate of the probability that the bet will win.
The key idea is that odds alone are not enough. To calculate expected value, you also need an estimate of the true probability of the outcome.
If your estimated probability is higher than the probability represented by the bookmaker's price, the calculation may produce positive EV. If it is lower, the expected value will be negative.
The full calculation compares the potential profit from winning with the amount lost when the bet fails.
When decimal odds are being used, the same calculation can also be written more simply.
Imagine a bookmaker offers decimal odds of 2.30 and you estimate that the outcome has a 50% chance of winning.
You decide to use a stake of €20.
The calculation is:
The result does not mean that you will make €3 on that specific bet. It describes the theoretical average value of the wager based on the probability estimate you entered.
A positive expected value means that, according to the probability estimate entered into the calculator, the betting price is higher than the price required to break even.
In this example, your estimate is higher than the probability represented by the bookmaker's odds. That difference is why the calculation produces positive expected value.
Negative expected value means the opposite. Based on the probability estimate entered, the price does not compensate for the risk of losing often enough.
For example, if the bookmaker offers odds of 2.00 but you believe the outcome has only a 45% chance of happening:
The calculator also converts your own probability estimate into theoretical fair odds.
For a 50% probability estimate:
In this example, your estimated fair price is 2.00 while the bookmaker is offering 2.30.
Entering 60% instead of 50% can dramatically change the EV result, but the calculator has no way to know whether either estimate reflects the true probability of the event.
This is the biggest limitation of expected value calculations. The formula itself is straightforward. Accurately estimating probability is the difficult part.
A bet can appear to have positive expected value simply because the probability entered into the calculator is too optimistic.
Expected value is a long-term mathematical concept. It does not predict the result of one individual event.
The outcome of one bet and the expected value of that bet are completely different questions.
Even a genuinely favorable price can lose repeatedly over a short sample. Variance does not disappear simply because a calculation produces positive EV.
Implied probability comes directly from the bookmaker's odds. Expected value requires another piece of information: your own estimate.
This comparison between the market price and your own probability estimate is the core of expected value analysis.
An EV calculator forces you to think about a betting price in terms of both probability and payout.
Instead of asking only, “How much can this bet win?”, the calculation asks a more important mathematical question: “Is the potential return large enough relative to the probability I assign to the outcome?”
It can be useful for understanding value betting, comparing different prices and seeing how even small changes in your probability estimate can dramatically change the expected result.